Question

for each pair of statements, choose the one that is true.
(a)

• ${e} in {e, f, g}$
• ${e}

subseteq {f, g, h}$
(b)

• ${12, 14, 16} in {2, 4, 6, 8, dots}$
• ${12, 14, 16} subseteq {2, 4, 6, 8, dots}$

(c)

• $5 in {4, 5}$
• ${5} in {4, 5}$

(d)

• $r subseteq {q, r}$
• ${r} subseteq {q, r}$

Explanation:

Step1: Analyze subset/membership (a)

• $\{e\} \subseteq \{e,f,g\}$ is true, but the option is marked wrong. $\{e\}$ has element $e$, not in $\{f,g,h\}$, so $\{e\}

subseteq \{f, g, h\}$ is true.

Step2: Analyze subset (b)

$\{12,14,16\}$ elements are all even numbers, so $\{12, 14, 16\} \subseteq \{2, 4, 6, 8, ...\}$ is true.

Step3: Analyze membership (c)

$5$ is an element of $\{4,5\}$, so $5 \in \{4, 5\}$ is true; $\{5\}$ is a set, not an element, so $\{5\} \in \{4, 5\}$ is false.

Step4: Analyze subset (d)

$\{r\}$ has element $r$ which is in $\{q,r\}$, so $\{r\} \subseteq \{q, r\}$ is true; $r$ is an element, not a set, so $r \subseteq \{q, r\}$ is false.

Answer:

(a) $\{e\}
subseteq \{f, g, h\}$
(b) $\{12, 14, 16\} \subseteq \{2, 4, 6, 8, ...\}$
(c) $5 \in \{4, 5\}$
(d) $\{r\} \subseteq \{q, r\}$